Note that the interpretation of the muon \(g-2\)  anomaly requires the 3-form field \(\Omega \)  to be relatively light and to have a moderately strong coupling to \(\mu \)  leptons, so that it should be well tested by the existing collider experiments. For example, if we extend this model by assuming that \(\Omega \)  has a universal coupling to all the SM leptons and quarks, the effective \(\Omega \) -gluon interaction could be inevitably generated via SM quark loops. Thus, the 3-form particle \(\Omega \)  can be produced at hadronic colliders such as the LHC mainly through the gluon fusion channel. By observing its decay products such as \(t\bar{t}\) , dijet, diphoton, diboson, and dileptons, such the universal coupling model with a light \(\Omega \)  has already been ruled out by the current ATLAS [1]}, [2]}, [3]}, [4]}, [5]} and CMS [6]}, [7]}, [8]}, [9]}, [10]}, [11]} data. On the other hand, if this 3-form field is leptophilic, i.e., \(\Omega \)  only couples to the SM lepton sector strongly, then the LHC constraints cannot be applied here. Nevertheless, with the assumption that \(\Omega \)  interacts with \(e^\pm \)  by a similar coupling to muons, such a model can be falsified in the near-future \(e^+e^-\)  colliders such as CLIC [12]}, [13]}, ILC [14]}, CEPC [15]}, [16]} and FCC-ee [17]}. Note that the cross section of \(e^- e^+ \rightarrow \mu ^- \mu ^+\)  mediated by \(\Omega \)  is given by
\(\sigma (e^- e^+ \rightarrow \mu ^- \mu ^+) = \frac{3 g_h^4}{\pi } \frac{s}{m_\Omega ^4}\,,\) 
